What happens to the electrons when an alpha particle is ejected from a
radioactive nucleus?

John Campbell, a physicist at the University of Canterbury, responded.

The total system is electrically neutral but the electrons have often shifted to other
atoms or places.

An alpha particle is an atom of helium that is stripped of its two electrons, ie it is
the nucleus of the helium atom. This is a remarkably stable entity.

A radioactive atom is one for which its nucleus is unstable and eventually
breaks down. When a radioactive nuclei decays by emitting an alpha particle,
the parent atom drops down two places in the chemical periodic table of
elements so now has two electrons too many. Where do they go?

The alpha particle comes out at very high speed because the energy involved
in a nuclear process is about a million times more than that of a chemical reaction.
The alpha particle is relatively massive and has a double electrical charge. As it
travels through air and material it rips electrons off those atoms. So there
is a trail of electrons and positively charged ions between the parent atom
and its alpha particle. The alpha particle had the energy to rip electrons
off of about a 100,000 atoms by which time it has slowed down so much it can
no longer do so. Then it attracts two electrons and becomes a neutral, inactive,
helium atom. Note that the whole trail, including
the parent atom and the alpha particle has zero net electrical charge so
eventually all the electrons in the trail recombine with atoms that are short of
a full complement of electrons, but not necessarily with the atoms they started with.

In electrically conducting materials this recombination occurs very quickly.
In air or a vapour there is a long enough time involved that the presence
of the otherwise invisible trail can be shown using a Wilson cloud chamber.

In some non-conducting materials, such as crystals of quartz, some of the
electrons get isolated from charged atoms and are stuck out of place until the
quartz is heated, at which time they can move to recombine with the charged atoms
and in doing so emit their stored energy as a flash of light. Because crystals
of quartz occur in clays, archaeologists use this technique (thermoluminsescence)
to date when pottery was made, or when it was last used for cooking.